Regionalized climate models using physics-informed neural networks

The present invention relates generally to the field of computing, and more particularly to machine learning. Extreme weather changes and impacts on the climate are increasing in the amount of changes that are occurring and in the complexity of weather patterns. Climate extremes can affect weather conditions and climate variability, both of which can have significant impacts on businesses and regions.

Embodiments of the present invention disclose a method, a computer system, and a computer program product for regionalized climate models. Embodiments of the present invention may include selecting a class of a reduced order model. Embodiments of the present invention may include building a neural network in a reduced order space. Embodiments of the present invention may include recovering full state dynamics. Embodiments of the present invention may include training a model. Embodiments of the present invention may include providing an output.

Detailed embodiments of the claimed structures and methods are disclosed herein, however, it can be understood that the disclosed embodiments are merely illustrative of the claimed structures and methods that may be embodied in various forms. This invention may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments set forth herein. Rather, these exemplary embodiments are provided so that this disclosure will be thorough and complete and will fully convey the scope of this invention to those skilled in the art. In the description, details of well-known features and techniques may be omitted to avoid unnecessarily obscuring the presented embodiments.

As previously described, extreme weather changes and impacts on the climate are increasing in the amount of changes that are occurring and in the complexity of weather patterns. Climate extremes can affect weather conditions and climate variability, both of which can have significant impacts on businesses and regions. Higher-fidelity regional climate models now exist, such as models with 1-10 km grid spacing, that offer some improvement to local climates. However, the current models have some critical issues, such as systematic errors in global climate models propagated into regional climate models due to a requirement of calibration of many model parameters. Another issue may include computational expenses that make the models impractical for high-impact climate resilience studies that require large sets of forecasts for uncertainty quantification and confidence scoring.

Surrogate models for fluid dynamics exist but these models present a unique challenge due to compressibility and having phase changes, such as from a gaseous state of water to a liquid state of water with resulting energy transfers. The fluid dynamics and phase changes are significantly more complicated than an incompressible Navier-Stokes computation. Current surrogate models for complex fluid flows, such as sparse identification of nonlinear dynamics (SINDy) make assumptions about or need to know the governing equations of the physical phenomenon that limits the model's applicability to very complex systems.

Physics-informed machine learning or artificial intelligence regional climate models solve computationally extensive calculations and cost a significant amount of money to build and operate. However, the current regional climate models may have unresolved issues, some include limitations on the model grid resolution and unsolved important sub-grid processes, such as turbulence and cloud convection. Additionally, the long computational time for physics-based climate models limit the ability for uncertainty quantification and exploration of how adaption measures can impact the future climate. Therefore, it may be advantageous to, among other things, provide new systems, methods and program products to intelligently regionalize climate models by creating advanced use of physics-informed neural networks.

The following described exemplary embodiments provide a system, a method and a program product for physics-informed machine learning. As such, embodiments of the present invention have the capacity to improve the technical field of physics-informed machine learning by creating improved regionalized climate models using physics-informed neural networks in the latent space. More specifically, a non-linear reduced order model or autoencoder is paired with a neural network in the latent space and with physics-informed partial differential equation (PDE) constraints. The created system, method and program product for physics-informed machine learning represents translating and visualizing the outputs of regionalized predictions and extremes for downstream impact models using dynamically created ontologies and knowledge graphs, such as the use of neuro-symbolic artificial intelligence.

According to an embodiment, a physics-informed artificial intelligence-based regional climate model may be built to emulate, as the use case provided herein, a climate system at high fidelity. The physics-informed artificial intelligence-based regional climate model may be trained using high fidelity weather and climate simulations. The physical constraints may be used to train the model and may ensure the model is retaining awareness of the physical system beyond interpolating between data points.

The regional climate model may perform rapid simulations. For example, estimates of the speedup of regional climate model simulations may be derived from a recent study of blood flow simulation using physics-informed artificial intelligence. The study identified a 2400× speedup compared to traditional simulation methods. Fast simulations may enable many scenarios to be generated, thus, fast simulations may enable a two-way interaction with downstream models and applications. For example, a physics-inspired downscaling of weather and climate models provide improved regionalized weather and climate information, short-term deterministic predictions with appropriate initial boundary conditions and long-term statistics that match the climate system.

Interpreting or understanding climate extremes and the ability to predict the impact of extreme weather will assist in developing highly effective climate-aware computing applications. The improved climate-aware computing applications and programs may enable resilient decision capabilities and policies for many industries or domains, such as supply chain, weather services, climate risk services, coastal infrastructure services, financial services, non-profit services, government services, legal services and technology services.

A regional climate model may be used for and during many phases of supply chain and logistics. For example, the pre-production phase, the production phase, the distribution phase and the end user or client consumption phase. Extreme weather patterns, such as floods, droughts or tropical cyclones have brought focus to supply chains and anticipating when regions may have extreme weather patterns that will benefit supply chain management. Many companies may be aware of climate related hazards and may be well informed about potential exposure to hazardous conditions, however, many lack an understanding of the vulnerability of alternate sourcing plans. The regional climate models or the regional climate program may provide an opportunity to bring an understanding to quantifying (e.g., fulfilling orders or sourcing critical components) the extreme climate events.

According to an embodiment, a regionalized climate program, system and method may learn the dynamics, such as weather phase changes, complex fluid flows or physical phenomenon in a reduced order space using a non-intrusive formulation. A non-intrusive formulation may make no assumptions about governing equations, which is important when the governing equations are non-tractable (i.e., complex or too complex), as they are for climate data.

Various types of machine learning models may be built and used to create predictive analytics and results for the various industries. The industry or domain provided herein as a use case is creating predictive data for extreme weather and climate events. Industries other than regionalized climate data predictions may include, for example, supply chain, medical, retail, entertainment, social media, business, technology, academic, government, industrial, legal or automotive. Machine learning models may also include deep learning models and artificial intelligence models.

Machine learning models may also include deep learning models, neural networks and artificial intelligence models. Training and updating a model may include supervised, unsupervised and semi-supervised machine learning procedures. Supervised learning may use a labeled dataset or a labeled training set to build, train and update a model. Unsupervised learning may use all unlabeled data to train a model. Semi-supervised learning may use both labeled datasets and unlabeled datasets to train a model.

A neural network may be a component of deep learning. A neural network may be related to or known as a deep network or a deep neural network. A neural network may interpret, label and classify raw data, such as unstructured data. A neuron in a deep neural network may combine input data and assign a weight to the input data based on a significance level of what the neural network is learning in order to classify the data. The deeper the neural network, the more neurons or node layers the input data passes through. A neuron, a node and a filter may be considered interchangeable terms. The neuron may represent the location that receives input data, produces and associates an input weight to the data and then determines, via a computation, if the data should continue or progress further in the network before the data is classified. Each layer of neurons may train the data based on the previous output layer. Autoencoders may be used as a type of neural network to ingest unsupervised data and to learn and encode the data. The autoencoder may learn how to represent ingested data as a dataset.

Deep learning is a type of machine learning that may classify information based on the training data. The training data may be structured data or unstructured data. Structured data may include data that is highly organized, such as a spreadsheet, relational database or data that is stored in a fixed field. Unstructured data may include data that is not organized and has an unconventional internal structure, such as a portable document format (PDF), an image, a presentation, a webpage, video content, audio content, an email, a word processing document or multimedia content. Deep learning may also be related to or known as hierarchical learning or deep structured learning.

Deep learning may map an input, classify data, interpret datasets and provide an output of data for one or more layers of data. Each layer of data may be represented as a node. A node may also be known as a neuron or an artificial neuron. Deep learning may detect similarities in data that may or may not be labeled. The deep learning models may provide, for example, a graph output that may be generated as nodes and edges relating to the domain specific taxonomy that is being learned.

Supervised learning and semi-supervised learning may incorporate feedback or ground truth by having an individual check the accuracy of the data, data labels and data classifications. Individuals are typically a subject matter expert who has extensive knowledge in the particular domain of the dataset. The subject matter expert input may represent ground truth for the model and the provided ground truth may raise the accuracy and the predictive capabilities of the model. The subject matter expert may correct, amend, update or remove the classification of the data or data labels by manually updating the labeled dataset. Using a subject matter expert to provide feedback to the model may improve the accuracy of the model as datasets are updated or corrected.

Referring to, an exemplary networked computer environmentin accordance with one embodiment is depicted. The networked computer environmentmay include a computerwith a processorand a data storage devicethat are enabled to run a software programand a regionalized climate program. The networked computer environmentmay also include a serverthat is enabled to run a regionalized climate programthat may interact with a databaseand a communication network. The computermay also be known as a client computer and the servermay also be known as a server computer. The networked computer environmentmay include a plurality of computersand servers, only one of which is shown. The communication networkmay include various types of communication networks, such as a wide area network (WAN), local area network (LAN), a telecommunication network, a wireless network, a public switched network and/or a satellite network. It should be appreciated thatprovides only an illustration of one implementation and does not imply any limitations with regard to the environments in which different embodiments may be implemented. Many modifications to the depicted environments may be made based on design and implementation requirements.

The computermay communicate with the servervia the communications network. The communications networkmay include connections, such as wire, wireless communication links, or fiber optic cables. As will be discussed with reference to, servermay include internal componentsand external components, respectively, and computermay include internal componentsand external components, respectively. The servermay also operate in a cloud computing service model, such as Software as a Service (SaaS), Analytics as a Service (AaaS), Blockchain as a Service (BaaS), Platform as a Service (PaaS), or Infrastructure as a Service (IaaS). Servermay also be located in a cloud computing deployment model, such as a private cloud, community cloud, public cloud, or hybrid cloud. Computermay be, for example, a mobile device, a telephone, a personal digital assistant, a netbook, a laptop computer, a tablet computer, a desktop computer, or any type of computing devices capable of running a program, accessing a network, and accessing a database. According to various implementations of the present embodiment, the regionalized climate program,may interact with a databasethat may be embedded in various storage devices, such as, but not limited to a computer/mobile device, a server, or a cloud storage service.

According to the present embodiment, a user operating a computeror a server(e.g., a server computer) may use the regionalized climate program,(respectively) to predict long-term realistic future climate conditions. The regionalized climate method is explained in more detail below with respect to.

Referring now to, a block diagram of example architecture for building a regionalized climate modelusing physics-informed neural networks in the latent space used by the regionalized climate program,according to at least one embodiment is depicted. The physics-informed neural network may include a deep learning model framework that solves forward and inverse weather and climate problems using nonlinear differential equations. A latent machine learning space may include compressed data representations when the represented data points are compressed to be shown closer in space. The architecture for building a regionalized climate modelmay include a coarse resolution climate model, a PINN-based ROMthat includes loss functions and a high-resolution long-term climate model.

A coarse resolution climate modelmay include a model that ingests or receives input data and provides variables in three dimensions as an output. For example, the input data that is provided to the coarse resolution climate modelincludes temperature data, wind speed data, wind direction data, air pressure data, air density data, humidity data or precipitation data. The output data from the course resolution model are temperature data, wind speed data, wind direction data, air pressure data, air density data, humidity data or precipitation data that is presented over time in three dimensions, such as latitude, longitude and height.

A PINN-based ROMmay stand for a physics-informed neural network (PINN) based reduced order model or reduced order modeling (ROM). The PINN-based ROMmay ingest data, for example, global climate data, and may provide high-resolution outputs of the ingested data. The components in the PINN-based ROMinclude a neural network, an encoder, a decoder and physics-informed constraints. The encoder (φ) may receive a state x(t) produced by the coarse resolution climate modeland may produce a latent state z(t). The neural network may provide latent dynamics ż(t) and may provide a latent space or data to the latent state z(t). The decoder (ψ) may receive the latent state z(t) and produce a reconstructed state {circumflex over (x)}(t). The encoder (φ) and the decoder (ψ) may select a type of reduced order model to use, such as a variational autoencoder or a principal component analysis (PCA). The neural network output of the latent dynamics ż(t) may include an output time-series of target variables in the latent space.

The PINN-based ROMmay include an autoencoder (i.e., encoder (φ) and decoder (ψ) with a neural network in a latent space. Typically, autoencoders, such as a sparse identification of nonlinear dynamics (SINDy) autoencoder performs a simultaneous discovery of reduced basis and parsimonious dynamics. The SINDy autoencoder produces effective coordinates and a parsimonious dynamical system model using linear sparse regression using a library of candidate terms.

The PINN-based ROMimproves the parsimonious dynamical system model using sparse regression by providing an autoencoder that replaces the sparse regression with a neural network. The neural network may include a fully connected neural network (i.e., a dense neural network), a long-short term memory (LSTM) reduced neural network, an echo state neural network or a liquid time-constant network. The neural network in the PINN-based ROMis also improved by including physics informed constraints in the loss function of the full order state. The neural network may provide greater flexibility by allowing the neural network to learn a shape function without any assumptions or constraints. Alternatively, the SINDy architecture requires a priori information (i.e., constraints) about the shape function that describes the latent space dynamics, such as the parsimonious model.

Generalizing to a reduced order model (ROM) or further generalizing the reduced order model (ROM) may include allowing the autoencoder to use any classical numerical method to find the reduced order basis (i.e., latent space). For example, one method may use the principal component analysis, another method may use the Karhunen-Loeve decomposition and another method may use the spectral proper orthogonal decomposition. The generalizing procedures of the autoencoder may replace the full order model with a reduced order model (ROM). The generalizing procedures of the autoencoder may find the reduced order basis that ensures reliable evaluation of the partial differential equation (PDE) system at a substantially reduced computational cost.

A high-resolution long-term climate modelmay predict long-term realistic climate statistics or may predict possible future states of the climate system. The high-resolution long-term climate modelmay represent the reconstructed state {circumflex over (x)}(t). For example, the reconstructed spatiotemporal prediction of target variables is produced, such as temperature, precipitation, wind speed and direction. The predictions include a realistic statistical distribution of future conditions that match long-term statistics. The predictions also include a deterministic prediction of future conditions if performing short-term weather forecasts.

The PINN-based ROMmay be an integral component in predicting the weather and climate conditions for both global and regional geographical areas. The global climate or the global climate system may target global circulation as simulated by a global climate model. For example, boundary conditions or features used are solar radiation, ocean and land surface processes or anthropogenic forcings, such as carbon dioxide, CO. The regional climate or the regional climate system may target regional circulation as simulated by a regional climate model. Data from a global model may be used to create predictions for a regional area. For example, boundary conditions or features are used from a global climate model, including ocean, land surface and anthropogenic forcings to create regional predictions.

The PINN-based ROMmay also be an integral component for predicting long-term climate statistics and short-term weather outcomes. For example, long-term realistic weather statistics generation is 1 month to 100 years. The multivariate output for the long-term predictions has realistic statistical distributions, including extreme weather events. The short-term example includes short-term weather predictions of 1 day to 30 days. The short-term predictions of expected weather over time may be deterministic.

Loss functions may be included in the PINN-Based ROMand may include data loss or partial differential equation (PDE) constraint loss. This includes additional improvements or novelty in that the loss calculation, or the loss computation is calculated for the state dynamics (i.e., full order solution) using physics-inspired constraints and for the latent dynamics (i.e., latent space) using data driven methods. Physics-inspired constraints may be applied to state dynamics and latent dynamics may be based on data, such as mean standard error or L2-norm. For example, the physics-inspired constraint is the residual of any partial differential equation that represents a dynamical system such as a plume model for atmospheric dispersion. Since the latent dynamics may not be known, the physics-informed constraints may be applied to the state dynamics and back propagated through the decoder to then be applied to the latent dynamics.

The loss functions or the data loss may include a loss in reconstruction, a loss in state dynamics, a loss in latent dynamics and a partial differential equation (PDE) loss. For example, the reconstruction loss is represented as

the loss in state dynamics ({dot over (x)}) is represented as

the loss in the latent dynamics (ż) is represented as

and the partial differential equation (PDE) loss is represented as

The loss functions may be represented as

The partial differential equation (PDE) loss may be defined by a partial differential equation (PDE) constraint. For example, partial differential equation (PDE) loss may be calculated using the advection-diffusion equation, R=∂C+∇·(Cu)−∇(K·∇C)−S, where C=C(x). The partial differential equation (PDE) loss may also be optimized to other loss functions, such as the Navier-Stokes equations, the Raleigh-Benard equations or convection, or the Boussinesq equation.

Referring now to, an operational flowchart illustrating the exemplary regionalized climate model building processused by the regionalized climate program,according to at least one embodiment is depicted. The regionalized climate model building processmay use physics-informed neural networks in the latent space, may predict latent space dynamics with physical constraints and may represent, translate and visualize the outputs. Additionally, the regionalized climate programmay predict weather or climate, or both, for global and regional global geographical areas and may predict long-term climate statistics and short-term weather outcomes.

At, a class of a reduced order model is selected. The class of the reduced order model may be selected based on the physics of the problem or the physics of the data (i.e., data physics), such as based on if the dynamical system is parabolic, hyperbolic or elliptical. The reduced order model may be used to obtain or to calculate latent dynamics. For example, proper orthogonal decomposition is used as a method to reduce the dimensionality of a spatiotemporal dataset. The reduced order model may include the components in the PINN-based ROM, such as an encoder and decoder (i.e., autoencoder) and a neural network to select a class of the reduced order model. For example, a class may include proper orthogonal decomposition, spectral proper orthogonal decomposition or autoencoders. A class may be selected by starting with a simple class of a reduced order model, such as a proper orthogonal decomposition. Next, autoencoders may be used as needed to predict target variables based on the skill of the system or the level of learning of the model.

According to an embodiment, the autoencoder may use nonlinear activation functions to encode the nonlinear properties of a dynamical system. An example of a dynamical system is the global atmospheric circulation. The autoencoder may be used to extract main features of a dynamical system in the latent space using the encoder and may recover the full state dynamics using the decoder.

At, a neural network is built in a reduced order space. A loss function may be selected for the reduced order space based on the physics of the problem or the physics of the data. The neural network may be built using a similar process as selecting the ROM, such as using an automatic hyperparameter optimization software framework. One example of a hyperparameter optimization software may include a framework such as Optuna. The neural network may also be built to predict a timeseries in the latent space, for example, using a long-short term memory recurrent neural network. The neural network may be deployed in the latent space to predict latent dynamics. Thus, no assumptions may be required relating to governing equations which is beneficial in complex systems, such as climate. The neural network may be used to predict the future timeseries of target variables in the reduced order space.

At, the full state dynamics are recovered. The loss function may be selected for the full order space (i.e., physics-inspired constraint). The loss functions may be included in or may be a part of the PINN-based ROM. The predicted full state dynamics is recovered using the reduced order model (ROM) decoder with the predicted time series and static basis functions of the reduced order model.

The physical constraints are selected based on the known partial differential equations that govern the weather system or the climate system, or both. The physical constraints may be used to drive the learning process of the model. A partial differential equation (PDE) based constraint may propagate physics from the full order space to the latent space using back propagation or automatic differentiation.

The partial differential equations (PDE) constraints may be encoded using back propagation to be consistent with dynamics in the latent space. In selecting the constraints, no assumptions may be required of the shape functions in the latent space. The back propagation or backwards propagation may be a training method for a neural network to evaluate the error function from the cost function. The error evaluated from the cost function may be propagated backwards through the neural network to update the neural network weights. For example, if the cost function includes information or data from the partial differential equations (PDEs), then the neural network remains consistent in the latent space. Including information or data from the partial differential equations (PDEs) may include the information about the physics of the system that is enforced during back propagation.

The shape functions may be determined by the neural network. The physics-informed partial differential equations (PDE) constraints may be included in the loss functions. The partial differential equations (PDE) loss may be computed for both the reconstructed state dynamics and the latent dynamics using back propagation through the decoder (ψ).

At, a model is trained. The model may be trained to predict long-term weather or climate statistics or short-term weather outcomes. The model may be trained to predict regional weather or climate and the output can be used as an input to downstream impact models. The predicted regional weather may include long-term weather statistics and the regional climate may include long-term climate statistics. The model being trained may include a high-resolution climate model (e.g., high-resolution long-term climate model).

For example, the PINN-based ROMmay be used to predict the weather, the climate, or both, for a region. The difference between the weather and the climate may be temporal. The weather may include short-term data and the model may provide short-term predictions, hours or weeks. The climate may include long-term data and the model may provide long-term predictions, such as months, decades or longer. An example incorporating a coarse resolution model (e.g., the coarse resolution climate model) may include predictions from a global climate model. The output of the coarse resolution model may be an input to the regionalized climate program,or the PINN-based ROM.

The model may be trained using dynamically created ontologies or knowledge graphs to represent or translate outputs of regionalized predictions. The model may be configured to downscale weather models and climate models. For example, the model or machine learning algorithms can be used to improved regionalized weather and climate data or information. Short-term deterministic predictions may be configured with appropriate initial conditions and boundary conditions. Long-term statistic predictions may be configured to match the climate system. The configuration of the model (e.g., to downscale or to forecast future conditions) may be determined by the feature or features and the target data. For example, if a short-term weather prediction is being determined, then the weather model data can be used as the feature inputs and target outputs. If climate statistics are being determined, then climate model data as inputs and outputs may be used.

At, outputs are provided. The trained model may provide representations, translations or visualizations, or a combination, of the outputs of the regionalized predictions and extremes for downstream impact models. The model output may provide a summarization of what is captured by the model based on deriving the interpretation of cause and effect from the latent space. The output may allow end users to interact with the model output without needing to run the model. For example, an end user may be able to find the effect of a rise in global temperature of x degrees on the average temperature of region R without actually running the model. The output may also provide a visualization of the learned latent space dynamics. For example, the spatial basis and timeseries in the latent space can be saved during model execution and then interrogated by a user utilizing the relevant decoder-encoder to discover the primary dynamical modes.